To solve a system of equations by elimination, make the coefficients of one variable equal. Subtract one equation from the other to solve for one variable, then substitute this solution into one of the original equations to solve for the other variable. In this case, the solution to the given system of equations is x = 3, y = 6.
Explanation:In mathematics, specifically in algebra, the method of elimination is used to solve a system of simultaneous equations. Your equations are:
2x -y = 03x - 2y = -3To solve this system by elimination, we need to make the coefficients of y in both equations equal by multiplying if necessary. We can obtain this by multiplying the first equation by 2:
4x - 2y = 0
3x - 2y = -3
Next, we subtract one equation from the other to eliminate y:
4x - 3x = 0 - (-3) => x = 3
To find y, substitute x = 3 into the first equation:
2*3 - y = 0 => y = 2*3 = 6
So, the solution to the system of equations is x = 3, y = 6.
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You want to buy a car. You have a choice of six different dealerships. Each dealership carries the same two car companies, and sells eight different models that all come in four colors. If you must choose one option from each of these four categories, how many different cars can you buy if you want a black or blue Hyundai?
There are 40 different ways could you choose a car black or blue Hyundai.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that Each dealership carries the same two car companies, and sells eight different models that all come in four colors.
The following steps can be used to determine the different ways could you choose a car:
Now Multiply 5 and 4 that is multiply five exterior color choices and six interior color choices.
5 x 4
Now Multiply the above expression with 2 that is with two model choices.
20 x 2
Further simplify the above expression.
= 40
There are 40 different ways could you choose a car.
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To determine the number of different Hyundais available in black or blue, you multiply the number of dealerships (6) by the number of Hyundai models (8) and the number of relevant colors (2), resulting in 96 different cars.
The question asks how many different cars you can buy if you want a black or blue Hyundai, given certain constraints. There are six dealerships, two car companies, eight models, and four colors available. To answer this, we calculate the total combinations possible with the given choices: dealerships (6), car companies (2), models (8), and colors (4). Since we are only interested in Hyundai cars in black or blue, we eliminate other colors and car companies from the choice set. The calculation is as follows:
Number of dealerships: 6
Car companies: 1 (only Hyundai)
Car models: 8
Car colors: 2 (black or blue)
To find the total number of possible combinations, we multiply the number of each category's choices together:
6 (dealerships)
* 1 (Hyundai)
* 8 (models)
* 2 (colors)
= 96 different cars
bought 5 ounces of raisins for $4 how much do raisins cost per ounce and how many ounces can you get for 1 dollar?
0.80 per ounce
1.25 ounces
In triangle ABC, the segments drawn from the vertices intersect at point G. Segment FG measures 6 cm, and segment FC measures 18 cm. Which best explains whether point G can be the centroid? Point G cannot be the centroid because 18:6 does not equal 2:1. Point G cannot be the centroid because FG should be longer than CG. Point G can be the centroid because 12:6 equals 2:1. Point G can be the centroid because FC is longer than FG.
Answer:
The correct explaination is Point G can be the centroid because 12:6 equals 2:1
Step-by-step explanation:
Given in triangle ABC, the segments drawn from vertices intersect at point G.
Segment FG measures 6 cm and and segment FC measures 18 cm.
FG = 6 cm & FC = 18 cm
and also FC = FG + GC
18 = 6 + GC ⇒ GC = 12
Note: The centroid divides each median in a ratio of 2:1
& 12:6 give rise to 2:1
Hence, the correct explaination for this is Point G can be the centroid because 12:6 equals 2:1
Answer:
C
Step-by-step explanation:
Suppose A and B represent two different school populations where A > B and A and B must be greater than 0. Which of the following expressions is the largest? Explain why. Show all work necessary. 2(A + B) (A + B)2 A2 + B2 A2 − B2
Answer:
The value for the expression [tex](A+B)^{2}[/tex] is the largest
Step-by-step explanation:
Since both A and B must be greater than 0 and A>B then we can assume the least possible values for B=1 and A=2.
So,
i) 2(A+B) = 2(2+1) = 2*3 = 6
ii) [tex](A+B)^{2}[/tex] = (A+B)*(A+B) = (2+1)*(2+1) = 3*3 = 9
iii) [tex]A^{2} + B^{2}[/tex] = [tex]2^{2} +1^{2}[/tex] = 4+1 = 5
iv) [tex]A^{2} - B^{2} = 2^{2} - 1^{2}[/tex] = 4-1 =3
Inspecting the answers of the above four expressions, we see that the value for the expression [tex](A+B)^{2}[/tex] is the largest.
Answer: (A+B)^2 is the largest because it equals 9 when A=2 and B=1 are plugged in and the rest are less than 9
Which is the graph of an odd degree root parent function?
Answer:
The correct answer is Option 4, the fourth graph
Step-by-step explanation:
We will go through why the other graphs are not the correct answer and then explain why the fourth is indeed the correct answer.
Option 1 is wrong because it has the general shape of the graph of an even valued function. These functions are either concave up or concave down.
Option 2 is wrong because it has the general shape of the cubic function. These functions are defined for both negative and positive values of x.
Option 3 is wrong because it is not defined for negative values of x. It has the general shape of the square root function.
Option 4 is correct because it has the general shape of the function [tex]f(x)=\sqrt[3]{x}[/tex]. Functions of this kind are defined for both negative and positive values of x.
Answer: the fourth Graph
Step-by-step explanation:
The system of equations y = -3x + 5 and y = 3x - 7 has
A. exactly one solution.
B. no solution.
C. infinitely many solutions.
D. exactly two solutions.
Answer:
This system will have a. exactly one solution.
Step-by-step explanation:
When two lines have different slopes it means that they intersect exactly one time.
If they have the same slope, we need to look at the intercept to see if there is none or infinitely many solutions.
However, these have different slopes and therefore have just 1 solution.
The given set of equations has exactly one solution as y = -1 and x = 2.
What is the equation?There are many different ways to define an equation. The definition of an equation in algebra is a mathematical statement that demonstrates the equality of 2 mathematical expressions.
To put it another way, the equation needs to be subject to some restrictions.
A linear equation could contain more than one variable. If a variable's maximum power constantly equals one, an equation is considered to be linear.
Given a set of equations,
y = -3x + 5 and y = 3x - 7
By equate,
-3x + 5 = 3x - 7
6x = 12
x = 2 and y = -1
Hence "The given set of equations has exactly one solution as y = -1 and x = 2".
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store owner decides to mark up all items by 30%. What is the selling price of an item that originally cost $10?
Answer:$13
Step-by-step explanation:
A recipe requires 1/4 lb of onions to make 3 servings of soup mark has 1.5 lbs of onions how amy sevings can mark make
During Christmas a book store sold 72 books. If the ratio of books to books marks sold was 9:2,how many bookmarks did the store sell
Answer:
16
Step-by-step explanation:
the 9 parts of the ratio is equivalent to 72 books
divide number of books by 9 to find one part of the ratio
[tex]\frac{72}{9}[/tex] = 8 ← 1 part of the ratio
2 parts = 2 × 8 = 16 ← number of bookmarks sold
Molly ran 2/3 of a mile in 8 minutes if molly rubs at that speed how long will it take. Her to run one mile
2x/3=8
2x=24
x=12
It takes Molly 12 minues to run one mile.
There are 230 calories in 4 ounces of a type of ice cream how many calories are in 6 ounces of that type of ice cream
Answer: at this amount, there are 57.5 calories per ounce
therefore, there are 355 calories in 6 ounces of this ice cream
(since 57.5×6=355.0)
Answer:
345 calories
Step-by-step explanation:
Total Calories = 230 calories
Total amount = 4 ounces
TO find how many calories in 6 ounces of the ice cream
For this question we have to find out the number of calories in one ounce of an ice cream firs
as it is given to us that 230 calories in 4 ounces
so no of calories in one ounce = total calories / no of ounces
=230 / 4
=57.5 calories / ounce
Now we know that their are 57.5 calories in one ounce of the ice cream
We have to find no of calories in 6 ounces of ice cream
No of calories = 6 * 57.5
=345 calories
so amount of calories in 6 ounces are 345 calories
Please help me out!!!!!!!!!!!!
Answer:
6.6% Would be the answer.
You can check by multiplying 1000 people by 0.06 and get 66 people which is the number of families for that survey.
If you can please mark brainliest ¯\_(ツ)_/¯
Step-by-step explanation:
Circle A has a radius with the length of 5 units. Calculate the exact length of the apothem, line segment AH . In your final answer, include your calculations.
ΔAED is the equilateral triangle. Therefore AH is a height of this triangle.
The formula of a height of an equilateral triangle:
[tex]h=\dfrac{a\sqrt3}{2}[/tex]
We have a = 5. Substitute:
[tex]\boxed{AH=\dfrac{5\sqrt3}{2}}[/tex]
You can use the Pythagorean theorem.
[tex]EH^2+AH^2=AE^2\\\\\left(\dfrac{5}{2}\right)^2+AH^2=5^2\\\\\dfrac{25}{4}+AH^2=25\\\\AH^2=25-\dfrac{25}{4}\\\\AH^2=\dfrac{100}{4}-\dfrac{25}{4}\\\\AH^2=\dfrac{75}{4}\to AH=\sqrt{\dfrac{75}{4}}\\\\AH=\dfrac{\sqrt{75}}{\sqrt4}\\\\AH=\dfrac{\sqrt{25\cdot3}}{2}\\\\\boxed{AH=\dfrac{5\sqrt3}{2}}[/tex]
If Circle A has a radius with the length of 5 units then the exact length of the apothem is 5√3/2
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Circle A has a radius with the length of 5 units.
We have to find the length of apothem
The formula of a height of an equilateral triangle
h=a√3/2
We have a = 5. Substitute:
h=5√3/2
Apply Pythagorean theorem.
(5/2)²+AH²=5²
25/4+AH²=25
AH²=25-25/4
AH²=75/4
Take square root on both sides
AH=5√3/2
Hence, if Circle A has a radius with the length of 5 units then the exact length of the apothem is 5√3/2
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What is the average rate of change of the function f(x)=5(2)^x from x = 1 to x = 5? Enter your answer in the box.
Answer:
37.5
Step-by-step explanation:
The average rate of change is the amount over an interval the outputs change in a ratio to the input change. In a linear function, this is constant and called slope. In all other function, it is called the average rate of change because the rate of change varies over the interval. We use the same formula for the average rate of change as we do slope. First we need both the inout and output values of the function over the interval.
For x=1, [tex]f(1)=5(2^1)=5(2)=10[/tex].
For x=5, [tex]f(1)=5(2^5)=5(32)=160[/tex]
Slope:[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We substitute [tex]x_1=1\\y_1=10[/tex] and [tex]x_2=5\\y_2=160[/tex]
[tex]m=\frac{160-10}{5-1}[/tex]
[tex]m=\frac{150}{4}=\frac{75}{2} =37.5[/tex]
Answer:
37.5
Step-by-step explanation:
Help with this question, please.
The limit of any constant function is the value of the constant, so the limit is just 5.
For this case we have that by definition:
The limit of a constant function of the form [tex]y = f (x)[/tex], where [tex]f (x) = c[/tex], is the same constant, whatever the value to which the limit tends.
Thus, the limit of "5" when x tends to "2", results in "5".
Answer:
5
Option A
Need help please thanks
Answers: (a→b), (b→a), (c→c)
Explanation:
Column A:
a) [tex]y = -3x + \dfrac{1}{3}[/tex]
m = -3 ⇒ m⊥ = [tex]\dfrac{1}{3}[/tex]
b) 6x - 2y = 4
-2y = -6x + 4
y = 3x - 2
m = 3 ⇒ m⊥ = [tex]-\dfrac{1}{3}[/tex]
c) y - 3 = [tex]\dfrac{1}{3}[/tex](x - 3)
m = [tex]\dfrac{1}{3}[/tex] ⇒ m⊥ = -3
Column B
a) y - 3 = [tex]-\dfrac{1}{3}[/tex](x - 3)
m = [tex]-\dfrac{1}{3}[/tex]
b) y = [tex]\dfrac{1}{3}x + 6[/tex]
m = [tex]\dfrac{1}{3}[/tex]
c) 3x + y = 3
y = -3x + 3
m = -3
******************************************************************************
Column A letter a matches to Column B letter b
Column A letter b matches to Column B letter a
Column A letter c matches to Column B letter c
An Electrician charges $30 for a service call plus $75 per hour of service. If he charged 210 how many hours did he work?
The school cafeteria needs to buy 200 new forks. If each package contains 9 forks, how many packages should the cafeteria buy?
Answer:
23 packages
Step-by-step explanation:
We are told that the school cafeteria needs to buy 200 new forks. Each package contains 9 forks.
To find the number of packages that school cafeteria should buy we will divide total number of needed forks by number of forks in each pack.
[tex]\text{The number of fork packages}=\frac{200}{9}[/tex]
[tex]\text{The number of fork packages}=22.22222[/tex]
Since forks come in package of 9, so cafeteria have to buy whole number packages.
Let us round up our answer to the whole number.
[tex]\text{The number of fork packages}=22.22222\approx 23[/tex]
Therefore, school cafeteria should buy 23 packages of forks.
Answer:
23 packages should the cafeteria buy.
Step-by-step explanation:
Proportion states that the two ratios or fractions are equal.
As per the statement: The school cafeteria needs to buy 200 new forks. If each package contains 9 forks.
then by definition of Proportion;
[tex]\frac{1}{9} = \frac{x}{200}[/tex] , where x represents the package
By cross multiply;
200 = 9x
Divide both sides by 9 we get;
[tex]\frac{200}{9} =\frac{9x}{9}[/tex]
Simplify:
[tex]x = \frac{200}{9} =22.222[/tex]
Therefore, 23 package should the cafeteria buy.
68% of 123 times 12 is?
Elena's aunt bought her a $150 savings bond when she was born. When Alayna is 20 years old the bond will have earned 105% interest how much will the bond be worth when Elena 20 years old?
Answer:
$307.5
Step-by-step explanation:
We have been given that Elena's aunt bought her a $150 savings bond when she was born. When Elena is 20 years old the bond will have earned 105% interest.
The bond's value after 20 years will be 150 plus 105% of 150.
[tex]\text{Bond's value when Elena will be 20 years old}=150+(\frac{105}{100}*150)[/tex]
[tex]\text{Bond's value when Elena will be 20 years old}=150+(1.05*150)[/tex]
[tex]\text{Bond's value when Elena will be 20 years old}=150+157.5[/tex]
[tex]\text{Bond's value when Elena will be 20 years old}=307.5[/tex]
Therefore, bond will be worth $307.5 when Elena will be 20 years old.
A die is rolled. What is the probability of rolling a 5 or a number greater than 3?
Probability of rolling a 5: 1/6
Probability of rolling a number greater than 3: 3/6
The probability of rolling a 5 or a number greater than 3 on a six-sided die is calculated by summing the individual probabilities of rolling a 4, 5, or 6, which are each 1/6. Therefore, the total probability is 3/6 or 1/2, equating to a 50% chance.
To solve this, we need to identify the favorable outcomes and divide them by the total number of possible outcomes. A six-sided die has six possible outcomes: {1, 2, 3, 4, 5, 6}. The event of rolling a 5 or a number greater than 3 includes the outcomes {4, 5, 6}. Hence, there are three favorable outcomes for the desired event (rolling a 4, 5, or 6).
The probability of any single outcome is 1/6, as there are six sides to the die. Therefore, the probability of rolling a 5 or a number greater than 3 is calculated by adding the probabilities of rolling each of these numbers:
Probability of rolling a 4 = 1/6Probability of rolling a 5 = 1/6Probability of rolling a 6 = 1/6Adding these probabilities gives us 3/6 or 1/2, making the probability of rolling a 5 or a number greater than 3 being 50%.
richard's annual take home pay is $34200. what is the maximum amount that he can spend per month paying off credit cards and loans and not be in danger of credit overload?
Given is :
The annual income of Richard = $34200
Hence, his monthly income becomes = [tex]\frac{34200}{12}[/tex] = $2850
So, the maximum amount that he can spend per month paying off credit cards and loans and not be in danger of credit overload can be a maximum of 20% of this income.
So, 20% of 2850 is = $570
Hence, approximately $570 can be spent a month.
As, the question has no options to choose from, but the question is complete in itself, so this is the best possible answer.
Answer: $570
Step-by-step explanation:
Please answer this question!! 50 points and brainliest!!
Answer:
x<=11
Step-by-step explanation:
2(x-3 ) <= 16
Distribute the 2
2x -6 <= 16
Add 6 to each side
2x -6+6<= 16+6
2x <= 22
Divide by 2
2x/2 <= 22/2
x<=11
The library has at least 5,000 books.Which inequality represents the number of book b at the library? A . B>5,000 B . B>=5,000
Noah made 12 \text{ kg}12 kg of trail mix for his family's hiking trip. His family ate 8600 \text{ g}8600 g of the trail mix on the hiking trip. How many grams of trail mix did Noah have left?
Answer:
3400 grams.
Step-by-step explanation:
We have been that Noah made 12 kg of trail mix for his family's hiking trip. His family ate 8600 g of the trail mix on the hiking trip.
Let us convert 12 kg into grams.
1 kg= 1000 grams
12 kg = 12*1000 grams =12000 grams.
Let u subtract 8600 from 12000 grams to find the amount of trail mix left.
[tex]\text{The amount of trail mix left}=12000-8600[/tex]
[tex]\text{The amount of trail mix left}=3400[/tex]
Therefore, Noah had 3400 grams left of trail mix.
In Circle O, secants ADB and AEC are drawn from external point A such that points D, B, E, and C are on Circle O. If AD=8, AE=6, and EC is 12 more than BD, find the length of AC.
The problem can be solved using the power of a point theorem. First, let BD = x and EC = x + 12. Construct an equation: 8x = 6(x+12). Solving for x gives BD = 9 and EC = 21. The length of AC is then 35.
Explanation:This problem can be solved using the concept of power of a point theorem in circle geometry. The power of a point theorem states that for any point outside a circle, the product of the lengths of the two line segments obtained by drawing secants from that point to the circle are always equal.
To apply this theorem to this problem, we'll first denote BD as x. Because the problem states that EC is 12 more than BD, we can denote EC as x + 12.
Now, using the power of a point theorem, we can write the equation (AD)*(DB) = (AE)*(EC). Substituting in the given values and the values we denoted for DB and EC, we get (8)*(x) = (6)*(x+12).
Solving this equation gives x = 9. Therefore, the length of BD is 9, and the length of EC is 21. To find the length of AC, we add the lengths AE, EC, and AD, which gives us AC = 6 + 21 + 8 = 35.
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A florist sold 15 arrangements in its first month of business. The number of arrangements sold doubled each month. What was the total number of arrangements the florist sold during the first 9 months? Enter your answer in the box.
Answer:
Step-by-step explanation:
Answer:
7665 arrangements
I need help please with this
What are the leading coefficient and degree of the polynomial 9-10x^2-2x-15x^4
Answer:
Leading coefficient = - 15
Degree = highest power on a variable = 4
Step-by-step explanation:
It might be easier to see if you rewrote the polynomial in the order it is normally presented.
Highest power goes on the left.
y = -15x4 - 10x^2 - 2x + 9
The leading coefficient (-15) is the number in front of the variable with the highest power (x^4 or 4)
The highest power on a variable is the degree.
If 3a= -9 ab = 15. What's the value of b
Answer:
b = -5
Step-by-step explanation:
So we know
3a = -9
Divide 3 on both sides
a = -3
Plug a in to the other equation
-3b = 15
divide -3 on both sides
b = -5